The following is an extract summary of the whole GFB Discussion Paper on the subject titled "Lightweight Under-Drive Pulley Kit Performance Testing" which is available for download below.
------------------------------------------------------Introduction

GFB’s range of Lightweight Under-Drive Pulley Kits are designed to improve
acceleration by reduce the rotational mass (inertia) on the crankshaft as well as parasitic loads from the driven accessories.

The pulleys are manufactured from 6061 T6 billet aluminium on the latest precision CNC machines, and typically save up to 2.5kg of weight over the factory pulleys.

Under-driving is achieved through the use of a smaller diameter crank pulley, which reduces the amount of drag from the accessories, particularly at high RPM. Note that GFB take care to ensure that accessory performance is not affected.

Discussion

The results shown above (refer article) are actually the pair of passes that show the smallest gains. Other tests could have been combined to show larger and better results, but this pair has the closest-matched conditions and represents the most honest results.

Gains or losses resulting from variations in boost pressure or ECU-related
adjustments are usually seen only in part of the rev range, as a bump or a dip, or a different shaped power/torque curve. The pair of runs chosen for comparison however, are very similar in shape, indicating that the engine is operating in as close to identical conditions as could be expected – the resulting improvement can therefore be said to be from the installation of the pulley kit only and not from external variations.

Conclusion

It can be seen in these results that fitting a GFB Lightweight Under-Drive Pulley Kit does in fact produce an honest, measurable and repeatable improvement in acceleration throughout the entire engine rev range.

The tests revealed that the minimum recorded improvements after replacing the factory pulleys with the GFB Lightweight Under-Drive Pulleys were:

The results charts all tell the same story, which is a consistent improvement in GForce throughout the 30-90 km/h test, which results in more power and consequently a faster time to 90km/h.

Importantly (especially on turbo engines), the G-Force improvement off-boost and during spool-up are enhanced by a much larger percentage because of the limited engine torque available at low RPM. This gives the car what can be best described as a noticeably “livelier” feel in the lower rev range, and a greater willingness to rev during acceleration.

This is unlike many other engine modifications that improve power through increased airflow, since such gains are usually only available for a portion of the rev range, and often the ECU is required to be re-tuned to suit. The GFB pulleys however offer their benefits independently of the engine tuning, and regardless of how much power it makes.